Heat a grill pan. In a large bowl, whisk the oil with the cumin and season with salt and pepper. Add the eggplants to the bowl and toss to evenly coat. Working in batches, grill the eggplants over moderate heat, turning, until tender, about 5 minutes per batch.

In a small bowl, mash the avocado with the lime juice. Spread the mashed avocado on the bottom buns. Top with the eggplants, cabbage, cilantro, and pickled jalapeños and carrots, close the buns and serve.

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